Time-varying stiffness of human elbow joint during cyclic voluntary movement

Abstract

The objective of this study was to determine the extent to which subjects modulate their elbow joint mechanical properties during ongoing arm movement. Small pseudo-random force disturbances were applied to the wrist with an airjet actuator while subjects executed large (1 rad) elbow joint movements. Using a lumped parameter model of the muscle, tendon and proprioceptive feedback dynamics, a time-varying system identification technique was developed to analyze the phasic changes in the elbow joint's mechanical response. The mechanical properties were found to be time-varying, and well approximated by a quasi-linear second-order model. The stiffness of the arm was found to drop during movement. The arm was always underdamped, with the damping ratio changing during movement. Inertia estimates were constant and consistent with previous measurements. Overall, the moving arm was found to be very compliant, with a peak stiffness value less than the lowest value measured during posture, and a natural frequency of less than 3 Hz. Changing the speed of movement, or the load from gravity, changed the stiffness measured, but not in strict proportion to the change in net muscle torque.

A model of open-loop control of equilibrium position and stiffness of the human elbow joint

“…5). The calculated K ilf values were well within the (wide) range of values reported in literature for static conditions (Lacquaniti et al 1982;Mussa-Ivaldi et al 1985;MacKay et al 1986;Flash 1987;Bennet et al 1992). Higher K ilf values were found when the combination of four individual muscle STIMs was optimized rather than the combination of two lumped STIMs.…”

“…Indeed, the K ilf values derived in this study were in the lower region of the wide range of total joint stiffness values (14-126 N m·rad −1 ) reported in the literature (e.g. Bennet et al 1992;Lacquaniti et al 1993;Gomi and Osu 1998). The large variation of stiffness values supports the claim of Latash and Zatsiorsky (1993) that neither the definition nor the experimental determination of stiffness is without problems.…”

“…For example, attempts to determine the (total) low-frequency joint stiffness using experiments in which subjects were asked to resist perturbations have resulted in values for elbow stiffness that range from 14 N m·rad −1 (Bennet et al 1992) to 126 N m·rad −1 (Lacquaniti et al 1982). Furthermore, separation of the reflexive and intrinsic contributions to the total low-frequency joint stiffness requires advanced system identification methods (e.g.…”

Identification of human joint mechanical properties from single trial data

“…We first tested the method described in Section II with data generated by simulating the changes in the human elbow joint dynamics from our previous studies [3], [20], which include the stiffness and damping changes in posture and movement. Fig.…”

“…Ensemble methods are promising [3], [14] because the results at any instant of time are supported by more data points. The methods align many trials with similar movement profile based on a feature in the movement profile to calculate an average movement.…”